Grondona is reportedly keen to keep Maradona in the role for a further four years but is understood to want to make changes to his backroom staff, but while Maradona is also eager to stay in the job he has threatened to step down if any changes are made.
The pair held the showdown talks on Monday night and with the president set to relay details of the meeting to members of the Argentinian Football Association board, the 49-year-old will discover his fate once the committee has come to a decision.
"Maradona told the AFA president his thoughts about the present and future and what he was expecting regarding his staff. The president's idea was the opposite and they discussed about that," said an AFA spokesman.
"After both parties expressed their own points of view, Grondona told Maradona that he was going to communicate his requirements to the members' executive committee in (Tuesday's) meeting and, according to the decision they make, then they were going to meet again.
"The meeting went through different moments. Some of them were kind, some others tense, but talking about football always.
"Only Maradona and Grondona attended the meeting. Gossip and speculation by the media are just theories and hypothesis and I cannot say anything about that.
"The executive committee will be given a spoken review of the meeting by Grondona and, according to what he reports, the committee will make a decision or they could even delay it."